WASHINGTON — Leaders of the Senate Foreign Relations Committee negotiated into the night on Monday to soften language and possibly shorten a congressional review period in legislation that would give Congress influence over the shape of President Obama’s nuclear accord with Iran.

The Iran Nuclear Agreement Review Act, Congress’s first legislative effort to muscle into the continuing talks to rein in Iran’s nuclear program in exchange for the lifting of economic sanctions, will formally go before the committee on Tuesday afternoon. Senator Bob Corker, Republican of Tennessee, the panel’s chairman, and Senator Benjamin L. Cardin of Maryland, its ranking Democrat, pushed to reach bipartisan consensus by Tuesday morning, then join forces to stave off threats to the bill from the right and the left.

A Democratic aide familiar with the negotiations said Monday night that Mr. Cardin was optimistic that a bipartisan accord would be reached by morning.

To try to get there, Mr. Corker and Mr. Cardin focused on watering down two provisions. One would require the president to certify every 90 days that Iran is not supporting terrorist attacks against Americans, an issue that has not been part of the nuclear negotiations. The other would prevent the president from waiving any sanctions until the expiration of a 60-day congressional review period.

The biggest threat to the bill still comes from Mr. Obama, who says the measure would undermine the international negotiations to rein in Tehran’s nuclear program. White House officials vowed on Monday that the president would “absolutely veto” the legislation in its current form, and he spent several hours on Monday discussing the Iran accord with Jewish leaders at the White House.

In two closed-door discussions in the Roosevelt Room, Mr. Obama sought to explain his initiative to Jewish leaders and longtime supporters of Israel, many of whom have expressed deep reservations about the effect of the Iran negotiations on Israel’s security. Aides said Mr. Obama hoped to enlist influential Jewish leaders in his bid to fend off a congressional vote on the still-unfinished nuclear agreement announced this month by Iran, the United States and six other world powers.

Republicans posed their own threat with amendments that would vastly complicate the nuclear talks. Senator Marco Rubio of Florida, fresh off his declaration Monday that he is seeking the Republican presidential nomination, will fly to Washington on Tuesday to push an amendment making any Iran deal dependent on Tehran’s recognition of Israel’s right to exist, which is considered a nonstarter.

In addition, the surviving former hostages who were held by Iran for 444 days, from late 1979 to early 1981 at the American Embassy in Tehran, have persuaded Senator Johnny Isakson, Republican of Georgia, to press for compensation as a condition to a final accord. Senator Ron Johnson, Republican of Wisconsin, would make the agreement a formal treaty requiring ratification by two-thirds of the Senate.

“My own feeling is I don’t understand the necessity of moving forward on legislation in the next 60 days,” said Representative Adam B. Schiff of California, the ranking Democrat on the House Intelligence Committee, after emerging from a two-hour, classified briefing for House members by three Obama cabinet secretaries. “Apart from a small domestic political benefit, I don’t see how it contributes to getting a better agreement or strengthening our bargaining position with Iran.”

Tom Zamora Collina, policy director at the Ploughshares Fund, an arms control group, said, “The worse this bill gets, the easier it gets for the president to veto it and for Democrats to sustain the veto.”

But Republican leaders are eager to confront the administration well before the June 30 deadline that has been set for a final accord. Senator John Cornyn of Texas, the No. 2 Republican in the Senate, said the bill would probably come to a vote this month, and Representative Kevin McCarthy of California, the majority leader, said Monday that he would push for quick passage of a Senate-approved bill.

Mr. Obama spent several hours Monday pitching the nuclear agreement in two private White House meetings as his aides began a furious, two-day lobbying effort on Capitol Hill aimed at heading off what they view as congressional interference.

Secretary of State John Kerry, Energy Secretary Ernest Moniz and Treasury Secretary Jacob J. Lew briefed House members in a classified session Monday evening. The officials are scheduled to hold a similar briefing for senators on Tuesday morning.

Jewish leaders who attended the first of the two White House sessions with the president said that Mr. Obama opened with a half-hour statement in which he provided a detailed, nine-point explanation of why he believes the nuclear deal with Iran is in the security interests of both the United States and Israel.

“His tone was very emphatic and very passionate,” said one official from a Jewish group who was briefed in detail on the discussion, and who asked for anonymity to discuss a private meeting at the White House. “He made the argument for why this is a good deal, and why he is not going down this road for the sake of bringing any harm to Israel.”

Critics in the room urged the president to push for a better deal, according to participants, saying it would allow Iran’s government to evade inspections of its nuclear facilities. And they told Mr. Obama that lifting sanctions would allow Iran to earn $100 billion from the sale of oil that would help finance terrorist activities around the globe.

Mr. Obama also acknowledged the strains in his relationship with Israel’s leadership, including Prime Minister Benjamin Netanyahu, but told the group that the disagreements were “not personal” and were instead evidence of serious policy disagreements, in particular about how to confront Iran’s nuclear ambitions.

Groups invited to the sessions included J Street, an organization that has been supportive of Mr. Obama’s negotiations with Iran, as well as the Union of Orthodox Congregations of America and the American Israel Public Affairs Committee, which oppose the deal. Other groups invited included the Anti-Defamation League, the American Jewish Committee, the Jewish Federations of North America and the Jewish Council for Public Affairs.

Officials said the first meeting with the president was intended for “leaders of American Jewish organizations,” while the second was for “Jewish community leaders.” Participants said the second meeting was reserved for wealthy supporters and donors, though Josh Earnest, the president’s spokesman, said that political contributions were “not a factor in their invitation.”

But the president’s opponents in this case include Democrats, nine of whom have co-sponsored the review act.

Democrats worry that the terrorism provision in the bill would, in effect, make the Iran agreement impossible to carry out. Supporters of the bill also worry that the 90-day review period would freeze the president’s hand for three months and give Iran time to back out of the deal.

A version of this article appears in print on , on Page A6 of the New York edition with the headline: Senate Leaders and White House Make Their Cases on Iran Deal Legislation. Order Reprints | Today’s Paper | Subscribe